As posted earlier, all of the tunes with the grayed out text and the dashed line circles are on both my iPhone and in iTunes. All play properly. So what's the difference? What do those circles and gray text really mean? They are evenly divided between songs purchased from iTunes Store and my own ripped tracks. Puzzlement.

All were playing correctly until yesterday when this lunacy repeated itself and all my tunes on the phone started disappearing and playing randomly again. Once again I sync'ed the phone with NO music. Then sync'ed again, adding selected playlists a few at a time. Once again, they continue to play correctly for now. I think there is some essential bug in iTunes that is causing this for hundreds of iOS users. My guess is that sooner or later Apple will discover the problem and fix it. But for now, a quick survey of the bulletin boards will show how widely this is being experienced.

Jerry, here's something that I just discovered. Or it's new. Or something.

If you device is showing in the Devices list in iTunes, and you select it, the sidebar will show two lists, Settings and On My Device. In either one, it seems you can choose what to sync.
Because I've been having strange issues with books (iBooks) on both my iPhone and iPad, I checked the On My Device section for a book that I finally got onto the two devices by downloading on the device. iTunes gave every indication that it was syncing the book in question, but it never showed up on the iPad or iPhone until I downloaded it there.

In the On My Device section in iTunes, the book is not listed, but I can add it. I can't actually test this out now because of having downloaded earlier on the iPhone.

Note that I did see some titles listed with dotted circles, and no way to figure out what that meant.

I also found that the settings for my iPhone were set to Selected Books instead of All Books. Either I did that by mistake while fiddling, or it happened spontaneously.

"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs